some result if resolution worked. Nothing
denotes that False was derived. Just means that
premises of proof state were extended.

mzero if rule could not be applied

Emulate a variant Isabelle's frule tactic. It works only if the given
maping of free variables of the rule makes the premise of the rule provable
under the given proof state. Then, the conclusion of the rule with free
variables mapped accordingly is added to premises of the proof state. The
last step works currently only for conclusions being false of pure
conclusions.

NOTE that frule works only for rules that contain no existential
quantifiers in the conclusion.